Question

Design a cartesian space trajectory planning system for a planar 2 link RR (link lengths are 1 meter each) robot that moves the TOOL from an initial position ($-.1 \quad 0.8$)$^T$ to final position ($-.1 \quad -.8$)$^T$ (w.r.t. base frame B which is assumed at $(0,0)^T$) along a straight line in 5 seconds. Set up all the equations properly. Determine and plot (use MATLAB) the joint space trajectory and velocity profile (use $J^{-1}$ for joint rates and INVKIN for joint values at an appropriate sampling rate) as a function of time. What happens to joint rates near a singularity? Explain why it happens? Suggest a possible mechanism to deal with it. Please refer to Equation 5.74 in your text for $J^{-1}$ and to Equations 4.16 and 4.27 for INVKIN.

          Design a cartesian space trajectory planning system for a planar 2 link RR (link lengths are 1 meter each) robot that moves the TOOL from an initial position ($-.1 \quad 0.8$)$^T$ to final position ($-.1 \quad -.8$)$^T$ (w.r.t. base frame B which is assumed at $(0,0)^T$) along a straight line in 5 seconds. Set up all the equations properly. Determine and plot (use MATLAB) the joint space trajectory and velocity profile (use $J^{-1}$ for joint rates and INVKIN for joint values at an appropriate sampling rate) as a function of time. What happens to joint rates near a singularity? Explain why it happens? Suggest a possible mechanism to deal with it. Please refer to Equation 5.74 in your text for $J^{-1}$ and to Equations 4.16 and 4.27 for INVKIN.

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